The government shutdown began Oct. 1—coincidentally, the same day the federal Obamacare exchange opened for Americans to enroll for health coverage or face a tax penalty for not signing up by early 2014. The partial closure of federal operations ended after 16 days with temporary deals to fund the government until Jan. 15 and extend the debt ceiling until Feb. 7.

"At the ending of the negotiations before the government shutdown, our last offer was just delay the [individual mandate] penalty for a year," Lankford said. President Barack Obama "shut down the government and went back to our previous statement and said, 'This is what they are holding out for.' No one heard what our last [Obamacare] offer was."

Lankford then argued that both Republicans and many Democrats now agree the health-care law isn't ready, adding, "That's where we were before the shutdown."